How a CDO is like a rectangular bathtub

July 15, 2009

J, at This is the Green Room, is in the middle of a series entitled “Deconstructing the Gaussian copula”. Part 1 was here, Part 3 is on its way, and Part 2 features a really good explanation of CDOs and default correlation:

To understand why tranching compounds the correlation problem, think of the CDO as a rectangular bathtub interspaced with mines that represent each issuer’s default. The CDO investors are aboard a boat on one side of the bathtub, and need to cross to the other side. If the boat hits a mine, that issuer defaults, and the explosion of the mine will damage the boat. The equity tranche has an extremely thin hull and will sink quickly; the senior tranche has a thick hull and can withstand many blasts without taking damage. Finally, the boat moves across the bathtub via geometric brownian motion – which is to say, randomly.

In a low-correlation world, the mines are dispersed uniform randomly across the bathtub; hitting one mine does not imply or necessitate hitting any other. With high correlation, the mines cluster somewhere in the water; hitting one mine makes it relatively certain that another will be hit.

As a consequence, equity investors prefer high correlation. They are indifferent to hitting just a few mines or many, as they are wiped out in both situations. Therefore, they prefer the mines to be clustered, as this leaves more clear paths across the bathtub. In contrast, senior investors prefer low correlation – they can withstand glancing off a few mines, but hitting a cluster would wipe them out.

This helps explain why leveraged super-senior trades turned out to be so much more dangerous than simple equity tranches with a similar expected return. When an equity tranche sinks, you lose a small, light dinghy. When a senior tranche sinks, you lose an aircraft carrier.

(Thanks to Charles Davì for the pointer.)

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